The NextRadio lock screen controls can be disabled by turning off notifications for the app.
Long press on the NextRadio controls in your notification tray when you have NextRadio running, and then tap the info icon that appears. This will take you to a screen where you can turn off notifications. You will no longer be able to control the radio from your notification tray, but it won't appear on your lock screen anymore.
If your device does not support the long press method of accessing notification controls, you can go into your Settings Menu, find Apps, and select NextRadio. There is a checkbox below the app title that turns on/off notifications.
Lock screen controls are common for all media players and are enabled by default, but if you already have a preferred lock screen and don't need to operate the radio from the lock screen, this is a convenient way to disable it.